Question

The tank at a gas station contained 400 gallons of gas. A tanker truck that contained 8,100 gallons of gas filled the station's tank. After that the tanker truck had 4 times as much gas as the station's tank. How much did the tanker truck put into the station's tank?

Answer 1

The tanker truck put 1300 gallons of gas into the station's tank.

Explanation:

Givens

• The gas station contained 400 gallons of gas.
• The truck contained 8,100 gallons of gas.
• After filling, the truck had 4 times as much gas as the gas station.

In this problem, the unknown variable
`x` represents the amount of gas the truck filled to the gas station. So,

`4(400+x)=8100-x`

`400+x` expresses the tank of the gas station filled

`8100-x` represents the amount of gas is taken out of the truck, which is the same amount that it's being filled to the station.

`4(400+x)` expresses the comparison between the gas station and the truck, the tank of the truck (after filling) is four times the tanks of the gas station.

Now, we solve for
`x`

`4(400+x)=8100-x\\1600+4x=8100-x\\4x+x=8100-1600\\5x=6500\\x=(6500)/(5)=1300`

Therefore, the tanker truck put 1300 gallons of gas into the station's tank.

Answer 2

1300

Explanation:

Let the amount put in the station's tank = x

4(400 + x) = 8100 - x Remove the brackets

1600 + 4x = 8100 - x Subtract 1600 from both sides

1600 - 1600 + 4x = 8100 - 1600 - x Do the subtraction

4x = 6500 - x Add x to both sides

4x + x = 6500 - x + x

5x = 6500 Divide by 5

5x/5 = 6500/5

x = 1300

1300 gallons were added to the station's tank.